Hi people I dont know if anyone can help, but I'm working on some models and I'm having a bit of difficulty with this one..

where is alpha is a const.

rate which no. of those infected changes depending on suseptibles getting ill and other recovering,

This process is described by

where beta is a const.

So i need to know how to form the differential equation for I(S) and given that I=1 when S=N, find solution for I(S).